The Kriging-based reliability analysis is extensively adopted in engineering structural reliability analysis for its capacity to achieve accurate failure probability estimation with high efficiency. Generally, the Kriging-based reliability analysis is an active-learning process that mainly includes three aspects: (1) the determination of the design space; (2) the rule of choosing new samples, i.e., the learning function; and (3) the stopping criterion of the active-learning process. In this work, a new learning function and an error-based stopping criterion are proposed to enhance the efficiency of the active-learning Kriging-based reliability analysis. First, the reliability-based lower confidence bounding (RLCB) function is proposed to select the update points, which can balance the exploration and exploitation through the probability density-based weight. Second, an improved stopping criterion based on the relative error estimation of the failure probability is developed to avoid the pre-mature and late-mature of the active-learning Kriging-based reliability analysis method. Specifically, the samples that have large probabilities to change their safety statuses are identified. The estimated relative error caused by these samples is derived as the stopping criterion. To verify the performance of the proposed RLCB function and the error-based stopping criterion, four examples with different complexities are tested. Results show that the RLCB function is competitive compared with state-of-the-art learning functions, especially for highly non-linear problems. Meanwhile, the new stopping criterion reduces the computational resource of the active-learning process compared with the state-of-the-art stopping criteria.

基于Kriging的可靠性分析在工程结构可靠性分析中被广泛采用，因为它具有以高效率实现准确的故障概率估计的能力。通常，基于Kriging的可靠性分析是一个主动学习过程，主要包括三个方面：（1）确定设计空间；（2）选择新样本的规则，即学习功能；（3）主动学习过程的停止标准。在这项工作中，提出了一种新的学习功能和基于错误的停止准则，以提高基于主动学习的基于克里格的可靠性分析的效率。首先，提出了基于可靠性的下置信界（RLCB）函数来选择更新点，通过基于概率密度的权重可以平衡勘探与开发。其次，基于故障概率的相对误差估计，提出了一种改进的停车判据，以避免基于主动学习克里金法的可靠性分析方法过早和过早地出现。具体而言，确定具有改变其安全状态的大概率的样品。由这些样本引起的估计相对误差被推导为停止标准。为了验证所提出的RLCB函数和基于错误的停止准则的性能，测试了四个具有不同复杂度的示例。结果表明，与最新的学习功能相比，RLCB功能具有竞争力，特别是对于高度非线性的问题。与此同时，